M=P^2/2KE: How is this derived?

I am just curious as to how this fits in. If momentum P=mv, and kinetic energy KE=1/2mv^2, how would one combine, derive, switch and swap (whatever the process is called), these two equations to end up with the formula m=P^2/2KE. It seems like a no-brainer, but I can't seem to make sense of the algebra.

It's fairly simple, no trickery involved. What does [tex]P^2[/tex] equal? Now, that almost looks like something you have with your kinetic energy equation. Can you convince yourself that [tex]KE = \frac{m^2 v^2}{2m}[/tex] is the same as your original equation? If so, simply plug in [tex]P^2[/tex]. From there, simply solve for m.